1. Field of the Invention
The present invention relates to the calibration of a force sensor mounted on an industrial robot.
2. Description of the Related Art
The calibration of a force sensor mounted on an industrial robot is conducted as a part of the manufacturing process after the force sensor is assembled. This precisely calibrated force sensor is mounted on the tip area of a band, such as a wrist flange, of a robot, and the robot is shipped from a factory in a form mounted with the force sensor.
Here, a conventional calibration of the force sensor is described with reference to FIG. 5.
A calibration stand 60 comprises a base 64, a firm 62 stood on the base 64, and a beam 66 one end of which is fixed to the upper end of the fulcrum 62. A force sensor 40 is mounted on an upper face 66a of the beam 66, and a calibration jig 68 is mounted on the force sensor 40. Further, a weight 70 is hung on the calibration jig 68 via a hanger 72.
The calibration of the force sensor 40 is operated by varying the magnitude of force and the moment applied to it by varying the posture of the force sensor 40 in which it is fitted to the calibration stand 60 and the total weight of the weight 70 in many ways.
The principle of the calibration will be described below with reference to the force sensor, which detects six axial forces comprising translational forces Fx, Fy and Fz in mutually orthogonal directions of Y and Z axes and axial moments Mx, My and Mz about these axes.
This force sensor for detecting the six axial forces has eight strain gages attached to the mechanistic section of the force sensor as a force detecting section, and these eight strain gages output voltages as detection signals from the force detecting section correspondingly to loads working on the force sensor.
The voltage output from the strain gages is denoted by v1, v2, . . . v8 and the output of the force sensor is denoted by the translational forces Fx, Fy and Fz together with the axial moments Mx, My and Mz as described above, and, further, a calibration matrix of conversion parameters for obtaining the power for force detection to be calculated from output signals from the force detecting section is denoted by C, and then the relationship among them is represented by equation 1.                                           [                                                            C11                                                  C12                                                  ⋯                                                  C18                                                                              C21                                                  C22                                                  ⋯                                                  C28                                                                              ⋮                                                  ⋮                                                                      xe2x80x83                                                                    ⋮                                                                              C61                                                  C62                                                  ⋯                                                  C68                                                      ]                    ⁢                      xe2x80x83                    [                                                    v1                                                                    v2                                                                    ⋮                                                                    v8                                              ]                =                  [                                                    Fx                                                                    Fy                                                                    Fz                                                                                      M                  ⁢                                      xe2x80x83                                    ⁢                  x                                                                                    My                                                                    Mz                                              ]                                    (        1        )            
When a known force Fx is applied to the force sensor 40, the relationship of equation 2 below is established using an unknown calibration matrix C.                     Fx        =                              [                                                            c11                                                  c12                                                  ⋯                                                  c18                                                      ]                    ⁢                      xe2x80x83                    [                                                    v1                                                                    v2                                                                    ⋮                                                                    v8                                              ]                                    (        2        )            
If this force Fx is varied in many ways and added m times (i.e. forces Fx1, Fx2 . . . Fxm are added) and the output of the strain gages (v11xe2x88x92v1m, . . . , v81xe2x88x92v8m) is measured each time, the relationship of equation 3 below will hold.                               [                                                    Fx1                                            Fx2                                            ⋯                                            Fxm                                              ]                =                              [                                                            c11                                                  c12                                                  ⋯                                                  c18                                                      ]                    ⁢                      xe2x80x83                    [                                                    v11                                            v12                                            ⋯                                            v1m                                                                    ⋮                                            ⋮                                                              xe2x80x83                                                            ⋮                                                                    v81                                            v82                                            ⋯                                            v8m                                              ]                                    (        3        )            
Equation 3 above can be rewritten into the following equation 3xe2x80x2.
FXT=c1TVxe2x80x83xe2x80x83(3)
Incidentally, in the above-mentioned equation 3xe2x80x2, matrices Fx, and c1 are:
Fx=[Fx1 Fx2 . . . FxM]T
c1=[c11 c12 . . . c18]T
And matrix V is represented by the following equation 4.                     V        =                  [                                                    v11                                            v12                                            ⋯                                            v1m                                                                    v21                                            v22                                            ⋯                                            v2m                                                                    ⋮                                            ⋮                                                              xe2x80x83                                                            ⋮                                                                    v81                                            v82                                            ⋯                                            v8m                                              ]                                    (        4        )            
The minimum approximate square solution of matrix c1 is determined by equation 6 as the c1 that minimizes the value of the following equation 5.
E2=(FxTxe2x88x92c1TV)T(xe2x88x92c1TV)xe2x80x83xe2x80x83(5)
c1T=FXTVT(VV-T)xe2x88x921xe2x80x83xe2x80x83(6)
In the above-described equation 6, VT(VVT)xe2x88x921 is a pseudo inverse matrix of a matrix V. Similarly, when the forces of the other elements than force Ex are applied at the same time and the output of the force sensor is recorded, the relationship of the equation 7 below is obtained.                               [                                                    Fx1                                            Fx2                                            ⋯                                            Fxm                                                                    Fy1                                            Fy2                                            ⋯                                            Fym                                                                    ⋮                                            ⋮                                                              xe2x80x83                                                            ⋮                                                                    Mz1                                            Mz2                                            ⋯                                            Mzm                                              ]                =                  "AutoLeftMatch"                                    [                                                                    C11                                                        C12                                                        ⋯                                                        C18                                                                                        C21                                                        C22                                                        ⋯                                                        C28                                                                                        ⋮                                                        ⋮                                                                              xe2x80x83                                                                            ⋮                                                                                        C61                                                        C62                                                        ⋯                                                        C68                                                              ]                        ⁢                          xe2x80x83                        [                                                            v11                                                  v12                                                  ⋯                                                  v1m                                                                              v21                                                  v22                                                  ⋯                                                  v2m                                                                              ⋮                                                  ⋮                                                                      xe2x80x83                                                                    ⋮                                                                              v81                                                  v82                                                  ⋯                                                  v6m                                                      ]                                              (        7        )            
or
F=CVxe2x80x83xe2x80x83(7xe2x80x2)
Incidentally, in equation 7xe2x80x2, F is a matrix represented by the following equation 8, comprising the output of the force sensor measured m times.                     [                                            Fx1                                      Fx2                                      ⋯                                      Fxm                                                          Fy1                                      Fy2                                      ⋯                                      Fym                                                          ⋮                                      ⋮                                                      xe2x80x83                                                    ⋮                                                          Fz1                                      Fz2                                      ⋯                                      Fzm                                      ]                            (        8        )            
Calibration matrix C given by the above-stated equation 7 or 7xe2x80x2 is to be found out by the following equation 9.
C=FVT(VVT)xe2x88x921xe2x80x83xe2x80x83(9)
In order to obtain the pseudo inverse matrix of matrix V, it is necessary and sufficient to apply to the force sensor such forces and moments as will give eight sets or more of linear independent strain gage outputs.
Calibration matrix C obtained in this way is stored and, when the robot is operated and forces are detected by the force sensor, the output from the strain gages of the force sensor (v1, v2 . . . v8) and this calibration matrix C are put into arithmetic operation of equation 1 to determine the translational forces Fx, Fy and Fz, and the moments Mx, My and Mz.
On the other hand, if an excessive load is applied to the force sensor and plastic deformation or the like occurs, the measuring accuracy will decrease, and according to the prior art it is necessary to dismount the force sensor from the robot temporarily and perform the above-described calibration again with the stand 60, calibration jig 68 and other members described above to find out a new calibration matrix C and store it. This not only entails much trouble but also may entail a slight mounting shift in the dismounting/remounting procedure because the force sensor fitted to a tip of the robot is dismounted and remounted. In particular, where the offset between the robot face plate and the tip of the tool is great, the shift of the tool center point (TCP) may often be too significant to ignore, necessitating fine adjustment in the teaching of the robot.
It is the object of the present invention to provide a force sensor permitting ready re-calibration while remaining mounted on the tip of the hand of the robot, so that, even if an accident such as a clash occurs to the force sensor while in use mounted on the robot, and the force sensor is overloaded as a result, with its mechanistic section plastic-deformed and measuring accuracy deteriorated, it can be subjected to simplified calibration entailing only minimal man-hours without requiring replacement.
To attain this object, according to the present invention, reference data for carrying out simplified calibration needing no dismounting of the force sensor from the robot are acquired and stored beforehand, and when re-calibration is needed because of a drop in measuring accuracy by any reason, the simplified calibration can be operated by utilizing the reference data.
The present invention makes it possible to carry out the re-calibration of the force sensor by utilizing tools for conventional use or other members without having to dismount the force sensor from the robot and without utilizing a weight or the like, whose weight and position of the center of gravity are precisely known, so that the force sensor can be easily restored to its normal state in a short period of time.